Which statement describes a z-score?

Which statement describes a z-score?

• A. It is the ratio of a data point to the mean.
• B. It measures how many standard deviations a value is from the mean.
• C. It is the distance between the max and min.
• D. It is the probability of observing that value.

Answer: (B)

A z-score tells you how many standard deviations a data point is from the mean. It is calculated as z = (x − μ) / σ, where μ is the mean and σ is the standard deviation. This standardization lets you compare values from different datasets or scales, since it places them on a common scale centered at zero with unit spread. A z-score of 0 means the value is at the mean; positive means above, negative means below. The other ideas don’t fit because they describe different concepts: a ratio to the mean ignores the spread of the data; the distance between the max and min is the range, another simple measure of spread; and a probability relates to how likely an outcome is under a distribution, whereas the z-score is a standardized value that can be used to find probabilities but is not itself a probability.

A z-score tells you how many standard deviations a data point is from the mean. It is calculated as z = (x − μ) / σ, where μ is the mean and σ is the standard deviation. This standardization lets you compare values from different datasets or scales, since it places them on a common scale centered at zero with unit spread. A z-score of 0 means the value is at the mean; positive means above, negative means below.

The other ideas don’t fit because they describe different concepts: a ratio to the mean ignores the spread of the data; the distance between the max and min is the range, another simple measure of spread; and a probability relates to how likely an outcome is under a distribution, whereas the z-score is a standardized value that can be used to find probabilities but is not itself a probability.